Saturday, January 2, 2016

Implement Heap


http://www.programming-algorithms.net/article/41909/D-ary-heap
d-ary heap behaves as a priority queue. Special case of d-ary heap (d=2) is binary heap.
D-ary heap is usually implemented using array (let's suppose it is indexed starting at 0). Than for every node of the heap placed at index n holds, that its parent is placed at index (n-1)/d and its descendands are placed at indexes d \\cdot k + 1, \\cdots ,\\, d \\cdot k + d. It is also convenient, if the heap arity is a power of 2, because than we can easily replace multiplications used in the tree traversal by binary shifts.
005.public class DAryHeap<ENTITY extends Comparable> {
006. 
007.private final static int EXPAND_RATIO = 2//how many times should be the underlying array expanded
008.private final static double COLLAPSE_RATIO = 0.25;//how empty must the heap be, to be the underlying collapsed
009.private Object[] array;
010.private int d; //parameter d
011.private int size; //size of the heap
012.private int initialSize;
013. 
014./**
015.* Constructor
016.* @param arraySize initial capacity of the heap
017.*/
018.public DAryHeap(int initialSize, int d) {
019.if (d < 2) {
020.throw new IllegalArgumentException("D must be at least 2.");
021.}
022.this.d = d;
023.this.array = new Object[initialSize];
024.this.initialSize = initialSize;
025.this.size = 0;
026.}
027. 
028./**
029.* Insert element into the heap
030.* Complexity: O(log(n))
031.* @param i element to be inserted
032.*/
033.public void insert(ENTITY i) {
034.if (array.length == size) {
035.expand();
036.}
037.size++;
038.int index = size - 1;
039.int parentIndex = getParentIndex(index);
040.while (index != 0 && i.compareTo(array[parentIndex]) < 0) {//while the element is less then its parent
041.array[index] = array[parentIndex]; //place parent one level down
042.index = parentIndex; //and repeat the procedure on the next level
043.parentIndex = getParentIndex(index);
044.}
045.array[index] = i; //insert the element at the appropriate place
046.}
047. 
048./**
049.* Return the top element and remove it from the heap
050.* Complexity: O(log(n))
051.* @return top element
052.*/
053.public ENTITY returnTop() {
054.if (size == 0) {
055.throw new IllegalStateException("Heap is empty");
056.}
057.ENTITY tmp = (ENTITY) array[0];
058.array[0] = array[size - 1];
059.size--;
060.if (size < array.length * COLLAPSE_RATIO && array.length / EXPAND_RATIO > initialSize) {
061.collapse();
062.}
063.repairTop(0);
064.return tmp;
065.}
066. 
067./**
068.* Merge two heaps
069.* Complexity: O(n)
070.* @param heap heap to be merged with this heap
071.*/
072.public void merge(DAryHeap<ENTITY> heap) {
073.Object[] newArray = new Object[array.length + heap.array.length];
074.System.arraycopy(array, 0, newArray, 0, size);
075.System.arraycopy(heap.array, 0, newArray, size, heap.size);
076.size = size + heap.size;
077.array = newArray;
078.//build heap
079.for (int i = newArray.length / d; i >= 0; i--) {
080.repairTop(i);
081.}
082.}
083. 
084./**
085.* Return index of the parent element
086.* @param index index of element, for which we want to return index of its parent
087.* @return index of the parent element
088.*/
089.private int getParentIndex(int index) {
090.return (index - 1) / d;
091.}
092. 
093./**
094.* Place the top of the heap at a correct place withing the heap (repair the heap)
095.* @param bottom last index of the array, which can be touched (is in the heap)
096.* @param topIndex index of the top of the heap
097.*/
098.private void repairTop(int topIndex) {
099.Comparable tmp = (Comparable) array[topIndex];
100.int succ = findSuccessor(topIndex * d + 1, topIndex * d + d);
101.while (succ < size && tmp.compareTo(array[succ]) > 0) {
102.array[topIndex] = array[succ];
103.topIndex = succ;
104.succ = findSuccessor(succ * d + 1, succ * d + d);
105.}
106.array[topIndex] = tmp;
107.}
108. 
109./**
110.* Return descendant with the least value
111.* @param from index of the first descendant
112.* @param to index of the last descendant
113.* @return index of the descendant with least value
114.*/
115.private int findSuccessor(int from, int to) {
116.int succ = from;
117.for (int i = from + 1; i <= to && i < size; i++) {
118.if (((Comparable) array[succ]).compareTo((Comparable) array[i]) > 0) {
119.succ = i;
120.}
121.}
122.return succ;
123.}
124. 
125./**
126.* Expand the underlying array
127.*/
128.private void expand() {
129.array = Arrays.copyOf(array, array.length * EXPAND_RATIO);
130.}
131. 
132./**
133.* Collapse the underlying array
134.*/
135.private void collapse() {
136.array = Arrays.copyOf(array, array.length / EXPAND_RATIO);
137.}
138. 
139.@Override
140.public String toString() {
141.StringBuilder builder = new StringBuilder();
142.for (int i = 0; i < size; i++) {
143.builder.append(array[i]).append(" ");
144.}
145.return builder.toString();
146.}
147.}


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